Direct Perturbation Method Research Articles

Solitons under perturbations

A direct perturbation method is developed in order to study the interactions of $N$ solitons with imperfections and with each other in the presence of imperfections. The leading-order effects are obtained directly from the $N$-soliton waveform without invoking methods from inverse-scattering theory. The method is based upon a Green's function and a "two time" procedure from classical perturbation theory. An example of a single soliton is developed in detail. Finally, this perturbation method is compared with other approaches in the literature.

An investigation of absorption‐reaction of carbon dioxide in liquid diethanolamine by the direct chromatographic perturbation method

AbstractPhysical and chemical equilibrium in the carbon dioxide‐diethanolamine system was studied by the direct chromatographic method. The amine was present as a coating on the inside of a capillary tube. Carbon dioxide‐helium mixtures were passed through the capillary until equilibrium was attained, at which time a sample of C14O2 was injected into the carrier stream. The retention volumes (carrier volume flowed at peak appearance) of concentration and radioactive perturbations were measured at four temperatures and five carrier gas compositions. Static equilibrium solubility of carbon dioxide in the amine was also measured to verify the dynamic results.The theory of reactive chromatographic flow was extended to this system. The concentration and isotope retention volumes, which theory predicts to be different functions of carrier composition, were shown to be self‐consistent. The static solubility data was also seen to be consistent with theory and with the direct chromatographic data. The liquid phase of the system appeared to be ideal except at infinite dilution of carbon dioxide. The apparent departure from ideality could be explained in terms of weak ionization of reaction products. Electrical conductivity measurements tend to confirm this hypothesis.Both physical and chemical equilibrium constants for carbon dioxide were obtained at the four temperatures. Gross heat of reaction and apparent ionization heat were also obtained.